‘If she makes this happen, I will do this thing’ … Neil Gaiman.
Photograph: Stephane Cardinale/Corbis via Getty Images

Neil Gaiman, bestselling author of American Gods and Neverwhere, has offered to stage a dramatic reading of Dr Seuss’s Fox in Socks, if fans pledge $1m (£769,000) to help refugees. The British author made the offer after accepting a previous challenge to read out the menu of a US dessert chain in exchange for $500,000-worth of pledges to the UN Refugee Agency (UNHCR).

The challenge to read the Cheesecake Factory menu was set on Friday by US comedian and author Sara Benincasa after what she described as an “inspiration blackout” following a date at the chain, and watching the new TV adaptation of American Gods.

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Gaiman responded in a tweet: “If she makes this happen, I will do this thing.” On his Facebook page, he added that he would read the Dr Seuss book if donations reached $1m. While donations are flooding into a fundraising page set up by Benincasa, they still have a way to go: at the time of writing, just under $17,000 had been raised. A deadline of 20 June – World Refugee Day – has been set.

Explaining why she set the challenge, Benincasa wrote: “There’s a reason he won an award for audiobooks, along with all the 18,000 other things he’s won as an author/screenwriter/producer/raconteur/hero.” As well as money from pledges, tickets will be sold for the reading and Benincasa said all ticket money would also go to the UNHCR. The event will also be live streamed.

Tagged #neilcake on Twitter, Gaiman has been set a challenging task with the Cheesecake Factory menu. The restaurant is known for its extensive and eclectic range, which extends to dishes such as “truffle-bacon cheesesticks”. The restaurant has joined the fundraising drive on social media, although it has yet to say how much it will donate to make it happen.

Gaiman was appointed a global goodwill ambassador of the UNHCR in February. After previously meeting with refugees in Syria and Jordan, he said that amid the horror, “there were many small and glorious stories of survival and hope, resilience and dignity”. He added: “If anyone could have the conversations I had, if only everyone could sit and speak to refugees, face to face, they would see that we really are the same, that we really are part of one family. And, at its best, a family does all it can to support each other.”